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Biopharmaceutics
PharmaceuticsPHM224Y/PHC330Y
Gregory Poon, Ph.D., R.Ph.
Biopharmaceutics
• Study of delivery of a drug to its intended site of action at the required rate and concentration
• Complex interplay of …• Physicochemical properties of the drug,• Dosage from,• Route of administration, and• Patho(physiology)
on the rate and extent of drug absorption
Biopharmaceutics
• Primary areas of focus • Rate of drug release/dissolution• Rate and extent of absorption
• Except for IV, all routes involve absorption of drug from site of administration
• Rate and extent of first-pass metabolism• Pharmacokinetics is a key set of parameters of a particular
dosage form of a drug, i.e.,• What is the time-dependent concentration of the drug at
a site after administering a particular dosage form?• Generally, we monitor blood concentrations
But why blood concentrations?
• Biological response is function of [drug] at site of action (dose-response curve)
• How to measure the latter in vivo?• Feasible ($)? Possible?
• In some cases, we can monitor the pharmacological response directly• Coagulation (warfarin, heparins, etc.)• BP, HR, etc. (antihypertensives, antiarrhymics, etc.)
• More often we use [drug] in blood as surrogate indicator of drug action• Also basis of therapeutic drug monitoring (TDM)
Blood
Plasma
Serum
Cells
Platelets, clotting factors
Dissolved ions, small molecules,
proteins
Review: separation of whole blood
Learning kinetics is useful!
• Chemical reactions• Drug metabolism
• Noncovalent transitions• Conformational transitions of proteins, DNA, etc.
• Movement between body compartments• Excretion of drug from blood to urine• Diffusion of gaseous anesthetic through alveoli
• Sterilization• Shelf life• Decay of radiopharmaceuticals• Once you’ve understood/modeled the mechanism, the
mathematics are all the same!
Basic kinetics review
• General form of a rate law for a reaction or transition involving n species
• k = rate constant• The reaction is y1
th order wrt X1, y2th order wrt X2, etc.
• yi = 0 (zeroth order; ν independent of [Xi])• yi = 1 (first order)• yi = 2 (second order), etc.
• The overall reaction order is
1 1 2 2 i
1
(productX X ...
[X
) sX
] i
kin
yi
i
y y y
kυ=
+ + + ⎯⎯→
= ∏
1
n
ii
y=∑
More kinetics review
• Rate law cannot be derived from stoichiometry of the balanced equation of a complex mechanism
• However for each elementary step yi does correspond to the stoichiometric coefficient
• In pharmacokinetics, we consider the movement and metabolism of a drug as elementary steps
• We assume that these steps are first-order
Dbloodrk⎯⎯→mk←⎯⎯ DurineMblood
bloodblood blood
[D ] ( )[D ] [D ]r m eld k k k
dtυ = − = + =
A Bk⎯⎯→
[A] [B
[A]( )
] A
?
[ ]d d kdt dt
t
− =
=
=
Properties of first-order reactions
The derivative is proportional to the function itself:what function has this property?
[A] [A]d kdt
= − Remember [A] = ƒ(t)
0
0
ƒ '( ) ƒ( )( ) ( )
[A]( ) ( )[A]
ln[A] ln[A]
cxcx
ct
kt
t C td le c le
dx
t c lee
kt
−
= ⋅
=
=
=
= −
l, c are constants
C is a constant
How much time does it take for A to decay by a fraction ℑ?
0 0
0.9
½
5ln 2
0
ln [A] ln[A]ln
ln
ln 0.9
ln 2
[A] 0.03125[A]
ktkt
tk
tk
tk
e
ℑ
ℑ
ℑ
−
ℑ = −ℑ = −
ℑ= −
= −
=
= =
Half-life
Ex: shelf life of a drug
After 5 half-lives
For first-order reactions, t½ is independent of concentration
Monoexponential decay corresponds to a one compartment model
A two compartment model
Volume of distribution
• A formal quantity, using blood volume as a reference to estimate drug distribution to tissues
Drug Vd (L/Kg) Vd (L, 70 kg)Sulfisoxazole 0.16 11.2 Phenytoin 0.63 44.1 Phenobarbital 0.55 38.5 Diazepam 2.4 168 Digoxin 7 490
Vd: Relationship to physiologic volumes
For 70 kg male
No seriously, where is all the drug hiding?
Area Under the Curve
• Another formal parameter
• 0 < a < t; t + Δt < b < ∞• If c(t) follows monoexponential decay
AUC ( )b
a ba
c t dt− = ∫
0
0DoseAUC p
d el el
cV k k−∞ = =
a b
Determining AUC empirically: trapezoid rule
The trapezoid rule is extremely crude as numerical analysis goes, but it’s only one that’s manually feasible
Non-IV routes involve an absorption phase
• Amount in GI tract
• Amount in plasma
• Even without solving the PDEwe’d expect a modalconcentration-time curvelike this:
Solving the PDEs
Effect of change in ka or F
Minimum Effective Conc.
MaximumSafe Conc.
tmax
cmax
t0Δt
Therapeutic index
Concentration-time curves: vocabulary
Okay this is correct now
Bioavailability
• Official definition (Shargel and Yu, 1995)• Rate and extent of active ingredient reaching systemic
circulation• Operational definition
• Fraction of a given administered dose that appears in systemic circulation
• Fraction absorbed × (1 – fraction metabolized)• AUC used to compare dosage form/route to IV (F = 1 by
definition)
unk
IV
AUCFAUC
=
Bioequivalence
• Two dosage forms of the same drug are bioequivalent if they have the same (relative) bioavailability• New vs. old formulation• Generic vs. brand name
• “Sameness” is a statistical measure• Ex: 90% CI
• AUC is again used as comparator
• Depending on dosage form and application, other parameters are also compared• tmax, cmax
test
ref
AUCFAUC
=
Multiple dosing regimes
• It’s true: we take some drugs more than once• Our assumptions
• One compartment model• Absorption/elimination parameters do not change
• ka, kel, F• Aim = quickly achieve and maintain desired steady state
• MEC < cp < MSC• Get it up, and keep it up
• Only two adjustable parameters• Dose (D)• Dosing interval (τ)
Multiple dosing: summary
• Average ss level determined by D, τ, and ka, and kel
• But ss peak and trough is determined by D only
• Implication for drugs with narrow therapeutic range• Time to ss depends on intrinsic kinetics only!
• Independent of D or τ• css will be different
• Limitations: many drugs exhibit saturable kinetics• Elimination becomes zero-order at high concentrations• Ex: Michaelis-Menten enzyme kinetics
max min
ƒ( , ,{ })ƒ( )
ss
ss ss
c D kc c D
τ=
− =
Physiology of drug absorption from GI tract
The small intestinal epithelium is highly folded
×3×10
×20
Molecular mechanisms of drug absorption
• Epithelial membrane is primary barrier GI content• Apical membrane on brush border
• Basolateral membrane• Transport occurs by
• Diffusion• Carrier-mediated (passive or active)• Pinocytosis (bulk transport)
Diffusion
• To first approximation, assume GI barrier is monolithic• Drug partitions (K1) from lumen into GI barrier, then
partitions (K2) into blood
• K always defined as [D]organic/[D]aqueous
• If drug is highly lipophilic (K >> 0) it partitions in membrane• If drug is highly polar or charged (K ~ 0) it remains in
lumen• How do we quantitatively describe this model?
Lumen GI barrier BloodK1 K2
Fick’s laws: introduction
• Describe flux J of matter across medium• Fick’s first law
• Describes steady state transportbehaviour
• D = diffusion coefficient [L2 t-1]• Fick’s second law
• “Nature abhors a wrinkle”
cJ Dx∂
= −∂
2
2
c cDt x
∂ ∂=
∂ ∂
Fick’s laws are widely applicable
• Drug movement across membranes• Dissolution of solid dosage forms• Gaseous anesthetics across alveoli• Transdermal movement of topically administered drugs• Ion movement in porous soil / concrete
• Geology, civil engineering• Doped ions in semiconductors
• Electrical engineering• Electrophoresis• Non-Fickian diffusion exists, but we’ll leave that to material
scientists
• Let’s assume [Dlumen] and [Dblood] independent of t (steady state)
• Fick’s first law describes flux across GI barrier of surface area A
Applying Fick’s law
1 lumen 2 blood( [D ] [D ])dc DA K KJ Ddx h
−= − =
lumen
h
blood
Mechanistic basis of first-order kinetics
• Now further assume that• K1 ~ K2 ≡ K (lumen and blood essentially aqueous)• [Dlumen] >> [Dblood] ~ 0 (sink conditions)
• First-order kinetics describes (simplified) diffusion kinetics!• Conversely if first-order kinetics is observed at all [Dlumen],
diffusion is predominant transport mechanism
lumen lumen[D ] [D ]DAKJ Ph
= =
Carrier-mediated transport
• Transmembrane protein carriers
Carrier-mediated transport: kinetic properties
• Saturability ensures deviation from first-order behaviour at high [Dlumen]
• Can use Michaelis-Menten equation to model kinetics
• Km and Vmax are intrinsic properties of carrier for given substrate (drug)
max lumen
lumen
[D ][D ]m
VJK
=+
maxlumen[D ]
m
VJK
= maxJ V=
[Dlumen] << Km [Dlumen] >> Km
Carrier mediated transport: energetics
• Energy (ATP) requirement• Active transport (against concentration gradient)
• Ex: riboflavin• Facilitated diffusion (along concentration gradient)
• More often facilitated diffusion is coupled cotransport• Indirectly ATP-burning• Symport or antiport• Popular cosubstrates
• Na+
• Glu, Gal• Di- / tripeptides• Acidic & neutral AAs
• H+
• Sucrose
S-A relationships in carrier-mediated transport
• Drugs that bear structural similarity to endogenous transporter substrate can often “hitch a ride”• Different Km, Vmax
Glucosamine Ceftriazone
Ramipril
Phagocytosis / Pinocytosis
• Bulk transport, often receptor-mediated• Material does not need to be dissolved
• Important for influx ofmacromolecules
• Contents oftenmetabolized inacidic vesicle
Physiological factors affecting bioavailability
• pH• Food (quantity, type)• Gastric emptying rate (GER)• Intestinal motility• First-pass metabolism
• Liver• Intestinal
• Intestinal efflux• P-glycoprotein (pgp)
• Ex: quinine, digoxin• You’ll cover most of these in PHM222Y, but we’ll go nuts
with pH• Most amenable to control in dosage form design
pH along GI tract
• Stomach• pH 1 to 3.5• Increases in presence of food• More acidic at night
• Small intestine• Duodenum pH 5 to 6• Lower ileum pH 8
• Large intestine• pH ~ 8
Ionization and absorption
• Presence of charge impedes partitioning into GI membrane• If drug is ionizable, presence of charge is pH-dependent
• Acid = uncharged at low pH• Base = uncharged at high pH
• Neutral molecules are well absorbed if not too polar• Drugs with permanent charges are often poorly or not at all
absorbed• Ex: quaternary ammonium
• Do you remember what anacid and a base is?
ipratropium
Acid-base definitions
• Brønsted-Lowry: proton transfer• Lewis: electron transfer• For our purposes, life occurs in aqueous environments
• ∴Proton transfers in water• A limited, operational definition
• Acid is a species/functional group that donates proton and becomes ionized
• Base is a species/functional group that accepts proton and becomes ionized
• Requires knowledge of chemistry of substance!• CanNOT be deduced only on the basis of its pKa!!!!!!
C CO
OH
HH
H
C CO
O
HH
H
Some acids
folic acid
Some bases
C NH2
CH2OHCH2OH
CH2OH
Tris
HCl
H2SO4
NaOH
NH4OHglucosamine Gentamicin
Some basic organic chemistry people like to forget
• Common acidic groups• Carboxylic acid (pKa 2-5)• Phenols (pKa ≈ 9)• Thiols (pKa ≈ 8)• α hydrogens
• Aliphatic alcohols are NOT acidic (pKa > 15)• MeOH, EtOH, etc.
• Some transition metals• Mn2+, Fe2+, etc.
• Nonmetal oxides (acid anhydrides)• CO2, SO3
• Common basic groups• Aliphatic amines (pKa 9-12)• Aromatic amines are much
weaker bases (pKa ∼ 5)• Amides are polar but NOT basic• Nitrogens in aromatic systems
(heterocycles) are often very weak bases or not at all
• Metal oxides (base anhydrides)• FeO, CaO, MgO, etc.
And some inorganic chemistry you ought to know
An imide,(weakly) acidic!
phenytoinNH:N
imidazole (pKa = 7.0)
N
pyridine (pKa = 5.25)
NH2
aniline (pKa = 4.63)
NH
pyrrole (pKa = 0)
NH
piperidine (pKa = 11.1)
Beispiel
Not every hydroxyl is acidic
And definitely not every nitrogen is basic
CH3 CO
NH2
pKa = 0.63
CH3CH2OH
pKa = 15.9
CO
OH
pKa = 4.2
OH
pKa = 9.89
NH
CCH2
O
CO
NH
O
barbituric acid (pKa = 4.01)
Ascorbate (pKa = 4.17, 11.6)
Brønsted-Lowry theory
+ -3
2+ -
+ -
(H O ) (A )(H O) (HA)
[H ][A ]55.6 [HA][H ][A ]
[HA]
aa aKa a
=
=
Activities!
Taking a(H2O) = 1; not everyone uses this standard state
[H2O] ≈ 56 M
+ -
+-
-
[H ][A ][HA]
[HA][H ][A ]
[A ]pH p log[HA]
a
a
a
K
K
K
=
=
= +
HA H+
A
CH3COOH CH3COO-H+
C NH3+CH2OH
CH2OHCH2OH
C NH2
CH2OHCH2OH
CH2OHH
+
+
+
+
pKa at 25°C
4.75
8.1
Tris base
+ - -3[HA] [H O ], [A ] [OH ]
Henderson-Hasselbalch
pH-partition hypothesis
• Developed by Brodie in 1950’s• For ionizable drugs, absorbed dose is determined by
extent of nonionization at given pH• Ionized fraction = not absorbed
But wait, is it really true?
• Pegs absorption on equilibrium properties, but GI tract is neither static nor closed
• Other factors are more important• Surface area of small intestine• Lipophilicity independent of ionization
• Perfusion ensures constant near-sink conditions against GI tract, so eventually entire dose will exit lumen as unionized drug … if given enough time in small intestine
• More exception than the rule
Pentamidine: pKa1,2 11.4